Automation has a service running on the computer which is the process that does all the printing work (and also executed the actions). What if this service is running under an account that does not have any rights on writing to the network location.

Please open the services (open Run / type "services.msc") and check the NiceLabelAutomationService to see under which user it is running. Check the column Log On As. If the user is Local System then double click the service and change the log on to an account which you know has network rights.

Just know that this is just an assumption what I think that the issue might be.